Summary Understanding the mechanisms regulating root development under drought conditions is an important question for plant biology and world agriculture.We examine the effect of osmotic stress on abscisic acid (ABA), cytokinin and ethylene responses and how they mediate auxin transport, distribution and root growth through effects on PIN proteins. We integrate experimental data to construct hormonal crosstalk networks to formulate a systems view of root growth regulation by multiple hormones.Experimental analysis shows: that ABA‐dependent and ABA‐independent stress responses increase under osmotic stress, but cytokinin responses are only slightly reduced; inhibition of root growth under osmotic stress does not require ethylene signalling, but auxin can rescue root growth and meristem size; osmotic stress modulates auxin transporter levels and localization, reducing root auxin concentrations; PIN1 levels are reduced under stress in an ABA‐dependent manner, overriding ethylene effects; and the interplay among ABA, ethylene, cytokinin and auxin is tissue‐specific, as evidenced by differential responses of PIN1 and PIN2 to osmotic stress.Combining experimental analysis with network construction reveals that ABA regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin.

BackgroundMany mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data of various forms. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology.MethodsBayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embeded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources of uncertainty.ResultsThe approach is demonstrated via application to a model of hormonal crosstalk in Arabidopsis root development, which has 32 rate parameters, for which we identify the sets of rate parameter values that lead to acceptable matches between model output and observed trend data. The multiple insights into the model’s structure that this analysis provides are discussed. The methodology is applied to a second related model, and the biological consequences of the resulting comparison, including the evaluation of gene functions, are described.ConclusionsBayesian uncertainty analysis for complex models using both emulators and history matching is shown to be a powerful technique that can greatly aid the study of a large class of systems biology models. It both provides insight into model behaviour and identifies the sets of rate parameters of interest.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-017-0484-3) contains supplementary material, which is available to authorized users.

• Patterning in Arabidopsis root development is coordinated via a localized auxin concentration maximum in the root tip, requiring the regulated expression of specific genes. However, little is known about how hormone and gene expression patterning is generated.• Using a variety of experimental data, we develop a spatiotemporal hormonal crosstalk model that describes the integrated action of auxin, ethylene and cytokinin signalling, the POLARIS protein, and the functions of PIN and AUX1 auxin transporters. We also conduct novel experiments to confirm our modelling predictions.• The model reproduces auxin patterning and trends in wild-type and mutants; reveals that coordinated PIN and AUX1 activities are required to generate correct auxin patterning; correctly predicts shoot to root auxin flux, auxin patterning in the aux1 mutant, the amounts of cytokinin, ethylene and PIN protein, and PIN protein patterning in wild-type and mutant roots. Modelling analysis further reveals how PIN protein patterning is related to the POLARIS protein through ethylene signalling. Modelling prediction of the patterning of POLARIS expression is confirmed experimentally.• Our combined modelling and experimental analysis reveals that a hormonal crosstalk network regulates the emergence of patterns and levels of hormones and gene expression in wild-type and mutants.

Plants are sessile organisms and therefore they must adapt their growth and architecture to a changing environment. Understanding how hormones and genes interact to coordinate plant growth in a changing environment is a major challenge in developmental biology. Although a localized auxin concentration maximum in the root tip is important for root development, auxin concentration cannot change independently of multiple interacting hormones and genes. In this review, we discuss the experimental evidence showing that the POLARIS peptide of Arabidopsis plays an important role in hormonal crosstalk and root growth, and review the crosstalk between auxin and other hormones for root growth with and without osmotic stress. Moreover, we discuss that experimental evidence showing that, in root development, hormones and the associated regulatory and target genes form a network, in which relevant genes regulate hormone activities and hormones regulate gene expression. We further discuss how it is increasingly evident that mathematical modeling is a valuable tool for studying hormonal crosstalk. Therefore, a combined experimental and modeling study on hormonal crosstalk is important for elucidating the complexity of root development.